Monday 3/26 Problems due on Tues 4/3

Transcription

1 8th Grade Spring Break Homework Name: Per: Monday 3/26 Problems due on Tues 4/3. Solve the system of equations: y = 4x - 3 y = -2x Use a graph to find x and y values that make both y = -⅔x + 3 and y = 2x - 5 true. 3. Diego has $ and begins saving $5 each week toward buying a new phone. At the same time that Diego began saving, Lin has $60 and begins spending $2 per week on supplies for her art class. Is there a week when they have the same amount of money? How much do they have at that time? 4. Solve the system of equations: y = 6x 4x + y = 7 5. Cici and Noah play a game in which they earn the same number of points for each goal and lose the number of points for each penalty. Cici makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points. a. Write a system of equations that describes Cici and Noah s outcomes. Use x to represent the number of points for a goal and y to represent the number of points for a penalty. b. Solve the system. What does your solution mean?

2 6. Write each fraction as a decimal Write each decimal as a fraction Arrange the following values from least to greatest: Tuesday 3/27 Problems due on Tues 4/3. Each of the six cards shows a shape. a. Which pair of cards shows a shape and its image after a rotation? b. Which pair of cards shows a shape and its image after a reflection? c. Which pair of cards shows a shape and its image after a translation? 2. Here are some points. a. What are the coordinates of D, E, and F after a reflection over the y-axis? b. Plot these points on the grid, and label them D, E, and F.

3 3. Describe a sequence of transformations to show that Triangle B is congruent to Triangle A. 4. Lines k and l are parallel, and the measure of angle ABC is 9 degrees. a. Explain why the measure of angle ECF is 9 degrees. b. What is the measure of angle BCD? Explain. 5. Write each expression as a single power of 0 6. Select all the expressions that are equivalent to 4-3 a. -2 b. 2-6 c. 4 3 d. ( 4 ) ( 4 ) ( 4 ) e. 2 f. ( 4 ) ( 4 ) ( 4 ) 7. Write each number in scientific notation (as a multiple of a power of 0) a. 42,300 b. 2,000 c. 9,200,000 d. Four thousand e. 80 million

4 8. For the pair of numbers below, circle the number that is greater. Then determine how many times bigger it is. 7 x 0 8 or 4 x Evaluate each expression. Use scientific notation to express your answer. Wednesday 3/28 Problems due on Tues 4/3. Here is a graph of the proportional relationship between calories and grams of fish: a. Write an equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories. b. Use your equation to complete the table: 2. Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y = 8x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps? How many more? 4 3. Select all the points that lie on the line y = 3 x + 5 a. (6,3) b. (2,33) c. (30,25) d. (99,37)

5 4. A contractor must haul a large amount of dirt to a work site. She collected information from two hauling companies. EZ Excavation gives its prices in a table. Happy Hauling Service gives its prices in a graph. a. How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning. b. Calculate the rate of change for each relationship. What do they mean for each company? c. If the contractor has 40 cubic yards of dirt to haul and a budget of $000, which hauling company should she hire? Explain or show your reasoning. 5. To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor. e. What is the equation of this line? a. How much would the painting company charge to paint a house that needs 20 hours of labor? A house that needs 50 hours? b. Draw a line representing the relationship between x, the number of hours it takes the painting company to finish the house, and y, the total cost of painting the house. c. Find the slope of the line. What is the meaning of the slope in this context? d. Find the y-intercept of the line. What is the meaning of the y-intercept in this context?

6 6. For each graph, calculate the slope of the line and then write the equation. 7. Select all the equations for which (-6,-) is a solution. a. y = 4x + 23 b. 3x = ½y c. 2x - 3y = d. 3y = ½x e. 2x + 6y = -6 Thursday 3/29 Problems due on Tues 4/3. Solve each of these equations. 2(x + 5) = 3x + 3y - 4 = 6-2y 3(n + 2) = 9(6 - n) 2. Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can t find it. Where is Clare s mistake and what is the solution to the equation? 3. Solve each of these equations and determine if the solution is No Solution or Infinitely Many Solutions. x - 3 = x + 3(x - 5) = 2(x - 5) + x x - 3 = 2x x

7 4. Write the other side of this equation so it s true for all values of x: ½(6x - 0) - x = 5. Write the other side of this equation so it s true for no values of x: ½(6x - 0) - x = 6. Select all the tables that represent functions. 7. Select all the graphs that represent functions. Friday 3/30 Problems due on Tues 4/3. This graph shows a trip on a bike trail. The trail has markers every 0.5 km showing the distance from the beginning of the trail. a. When was the bike rider going the fastest? b. When was the bike rider going the slowest? c. During what times was the rider going away from the beginning of the trail? d. During what times was the rider going back towards the beginning of the trail? e. During what times did the rider stop?

8 2. Three cylinders have a height of 8 cm. Cylinder has a radius of cm. Cylinder 2 has a radius of 2 cm. Cylinder 3 has a radius of 3 cm. Find the volume of each cylinder. 3. A cone has volume 2π cubic inches. Its height is 4 inches. What is its radius? 4. Sphere A has radius 2 cm. Sphere B has radius 4 cm. a. Calculate the volume of each sphere. b. The radius of Sphere B is double that of Sphere A. How many times greater is the volume of B? 5. Select all the expressions that are equivalent to 0-6 a. b. c d e. ( 0) f Decide whether each number in this list is rational or irrational 7. Estimate 7 37 to the nearest tenth. 8. Plot each number of the number line:

9 9. Evaluate each cube root Find the positive solution to each equation. If need, estimate your solution to the nearest tenth. x 2 = 8 x 3 = 8 x 2 = 5 Extra Credit Problems due on Tues 4/3. Triangle DEF is a dilation of triangle ABC with scale factor 2. In triangle ABC, the largest angle measures 82º. What is the largest angle measure in triangle DEF? Is it 82º or 64º? Explain. 2. The graph show the high temperatures in a city over a 0-day period. a. What was the high temperature on Day 7? b. On which days was the high temperature 6 degrees? c. Is the high temperature a function of the day? Explain how you know. d. Is the day a function of the high temperature? Explain how you know. 3. Jada fills her aquarium with water. The graph shows the height of the water, in cm, in the aquarium as a function of time in minutes. Invent a story of how Jada fills the aquarium that fits the graph.

10 4. Use the graph below to answer the questions that follow. a. Draw a line that you think is a good fit for this data. b. Use your line of best fit to estimate what you would expect the y-value to be when x is 0. c. Which of these statements is true about the data in the scatter plot? i. As x increases, y tends to increase. ii. As x increase, y tends to decrease. iii. As x increases, y tends to stay unchanged. 5. Select all the relations that are functions a. {(-7,20), (3,5), (0,5), (-2,0), (6,-4), (-6,-9), (4,4)} b. c. d. y = 3x + 6. Select all the equations that are linear. a. y = ½x - 5 c. x + y = 4 b. 2x - 3y = 20 d. x = 2y -